Black holes, equilibrium and cosmology

We trace the origins and development of black hole thermodynamics across the past half-century, emphasizing the framework’s relation to classical thermodynamics, and the vital role played by the notions of equilibrium, stationarity and symmetry. We discuss different interpretations of the first law of black hole mechanics, and assess the validity of its mechanical, process-based interpretation for evaporating black holes. We bring these ideas to the cosmological realm, and highlight the various difficulties that arise when formulating thermodynamics for black holes in asymptotically de Sitter backgrounds. We discuss a number of proposed solutions and the open questions that arise therein.